3-6 Compound Inequalities Compound Inequality Two distinct inequalities joined by the word and or the word or. The graph of a compound inequality with the word and contains the overlap of the graphs of the two inequalities that form the compound inequality. The graph of a compound inequality with the word or contains each graph of the two inequalities that form the compound inequality.

3-6 Compound Inequalities You can rewrite a compound inequality involving and as a single inequality. For example: x  3 and x ≤ 7 can be written as 3 ≤ x ≤ 7 You read this as “x is greater than or equal to 3 and less than or equal to 7” or “x is between 3 and 7, inclusive”

3-6 Compound Inequalities A solution of a compound inequality involving and is any number that makes both inequalities true. How do you solve AND compound inequalities? You can solve a compound inequality involving and by: Separating it into two inequalities and solving each or By working on all three parts of the inequality at the same time. You work to isolate the variable between the inequality symbols.

3-6 Compound Inequalities A solution of a compound inequality involving or is any number that makes either inequality true. How do you solve OR compound inequalities? To solve a compound inequality involving or you MUST solve separately the two inequalities that form the compound inequality.

3-6 Compound Inequalities Interval A portion of the number line. Interval notation A way to describe an interval on the number line that includes the use of three special symbols.

3-6 Compound Inequalities What are the three special symbols for interval notation? Parentheses: Use ( or ) when a < or > symbol indicates that the interval’s endpoints are NOT included. Brackets: Use [ or ] when a  or  symbol indicates that the interval’s endpoints are included. Infinity: Use  when the interval continues forever in a positive direction. Use – when the interval continues forever in a negative direction.